Spectral imbalance in the inertial range dynamics of decaying rotating turbulence

Abstract

Direct numerical simulations of homogeneous decaying turbulence with mild background rotation show the existence of a systematic and significant imbalance between the non-linear energy cascade to small scales and its dissipation. By starting the decay from a statistically stationary and fully developed rotating turbulence state, where the dissipation and the energy flux are approximately equal, the data shows a growing imbalance between the two until a maximum is reached when the dissipation is about twice the energy flux. This dichotomy of behaviours during decay is reminiscent of the non-equilibrium and the equilibrium regions previously reported for non-rotating turbulence [P.C. Valente, J.C. Vassilicos, Phys. Rev. Lett. 108 214503 (2012)]. Note, however, that for decaying rotating turbulence the classical scaling of the dissipation rate ǫ ∝ u ′3 /L (where u ′ and L are the root mean square fluctuating velocity and the integral length scale, respectively) does not appear to hold during decay, which may be attributed to the effect of the background rotation on the energy cascade. On the other hand, the maximum energy flux holds the scaling Πmax ∝ u ′3 /L in the initial stage of the decay until the maximum imbalance is reached.

Condensates in rotating turbulent flows

“…Thus, in the presence of strong rotation, fluid motions that are invariant along the direction of rotation (often referred as the slow manifold) become isolated from the remaining flow and if forced they dominate leading to the quasi-2D behaviour (Chen et al 2005;Scott 2014). This quasi-2D behaviour has been realized in experiments (Ibbetson & Tritton 1975;Hopfinger et al 1982;Dickinson & Long 1983;Baroud et al 2002Baroud et al , 2003Sugihara et al 2005;Ruppert-Felsot et al 2005;Morize & Moisy 2006;Staplehurst et al 2008;van Bokhoven et al 2009;Yoshimatsu et al 2011;Machicoane et al 2016) and numerical simulations (Yeung & Zhou 1998;Smith & Waleffe 1999;Godeferd & Lollini 1999;Chen et al 2005;Thiele & Müller 2009;Mininni et al 2009;Mininni & Pouquet 2010;Favier et al 2010;Sen et al 2012;Marino et al 2013;Alexakis 2015;Biferale et al 2016;Valente & Dallas 2017). These arguments however have various limitations.…”

Cascades and transitions in turbulent flows

“…This is qualitatively and quantitatively summarized in Fig. (65) where we show the results for the local energy dissipation, ν|∇u| 2 and enstrophy |w| 2 on a 2D cut of a 3D turbulent flow, together with their PDF.…”

“…Rotation has been the focus of many studies in turbulence research and modeling [256,257]. The quasi-2D behaviour has been realized in experiments [49][50][51][52][53][258][259][260][261][262][263][264][265] and numerical simulations [38,[54][55][56][57][58][59][60][61][62][63][64][65]. A visualization of a 2D cut from the rotating experiment [266] is shown in Fig.…”

Critical transition in fast-rotating turbulence within highly elongated domains

“…The formation of large-scale quasi-2-D structures in rotating flows was observed early on in experiments (Ibbetson & Tritton 1975; Hopfinger, Browand & Gagne 1982; Dickinson & Long 1983) and numerical simulations (Bartello, Méties & Lesieur 1994; Yeung & Zhou 1998; Godeferd& Lollini 1999; Smith & Waleffe 1999). Since then, various investigations have focused on different aspects of the quasi-2-D behaviour of rotating turbulence experimentally (Baroud et al 2002, 2003; Morize & Moisy 2006; Staplehurst, Davidson & Dalziel 2008; Van Bokhoven et al 2009; Duran-Matute et al 2013; Yarom, Vardi & Sharon 2013; Machicoane, Moisy & Cortet 2016) and numerically (Mininni, Alexakis & Pouquet 2009; Thiele & Müller 2009; Favier, Godeferd & Cambon 2010; Mininni & Pouquet 2010; Sen et al 2012; Marino et al 2013; Biferale et al 2016; Valente & Dallas 2017; Buzzicotti et al 2018 a ; Buzzicotti, Clark Di Leoni & Biferale 2018 b ). In particular, recent experiments were able to investigate the presence of the inverse cascade (Campagne et al 2014, 2015, 2016; Yarom & Sharon 2014).…”